What defines matching topology?
Several things matter:


The vertex count must be the same. = (v0...v19)
The edge list must have the same vertex indices to build each edge. That is, the same vertices must be connected. = [[v0,v1],...[v10,v11],[v18,v19]]
The polygon list must have the same vertex indices to build each face. That is, each face must be formed by the same vertices, in the same order. = [[v14,v15,v7,v4],...[v7,v6,v18,v19]]


Basically, you can move the vertices all you like, but you can't change how they connect.

Here is an image to demonstrate a deformation: